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The length of the perpendicular drawn...

The length of the perpendicular drawn from `(1,2,3)` to the line `(x-6)/3=(y-7)/2=(z-7)/(-2)` is a. `4` b. `5` c. `6` d. `7`

A

4

B

5

C

6

D

7

Text Solution

Verified by Experts

The correct Answer is:
d
Let P be the point (1,2,3) and PN be the length of the perpendicular from P on the given line.
Coordinates of point N are `(3lamda+6,2lamda+7,-2lamda+7)`.
Now PN is perpendicular to the given line of vector
`3veci+2vecj-2veck`. Thus,
`3(3lamda+6-1)+2(2lamda+7-2)-2(-2lamda+7-3)=0orlamda=-1`
Then, point N is (3,5,9)
`impliesPN=7`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  2. Let L be the line of intersection of the planes 2x""+""3y""+""z""="...

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  3. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

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  4. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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  9. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  10. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4z...

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  11. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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  12. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  13. Two system of rectangular axes have the same origin. IF a plane cuts t...

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  14. Find the equation of a plane which passes through the point (3, 2, 0...

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  15. The dr. of normal to the plane through (1,0,0), (0,1,0) which makes an...

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  16. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

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  17. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c ...

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  18. Distance of the point P(vecc) from the line vecr=veca+lamdavecb is

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  19. From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to...

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  20. The plane vecr cdot vecn = q will cotain the line vecr = veca + lambda...

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